## PUZZLES

(Set – 46)

## PUZZLE—1

There are seven students namely, P, Q, R, S, T, U and V, who scored different percentage of marks in HSC exam (in %) among- 65, 72, 73, 79, 86, 89 and 93. They also scored different percentage of marks from each other in SSC exam. In HSC exam, T scored 7% more than that of U in HSC exam. Sum of the percentage of marks scored in HSC and SSC exams by U is 162, which is same as that of P. In HSC exam, the difference in the percentage of marks scored by T and P is 14. The student, who scored highest percentage of marks in HSC exam, scored 1% less in his SSC exam than that of P in SSC exam. Sum of the percentage of marks scored in HSC and SSC exam by S is 1% more than the sum of percentage of marks scored in HSC and SSC by the student who scored highest marks in HSC exam. In HSC exam, S scored 16% more than some other student in HSC exam. Sum of the percentage of marks scored in HSC and SSC exam by V is 164 and he is not the lowest scorer in HSC exam. In HSC exam, R scored more percentage of marks than Q in HSC exam. In SSC exam,the sum of the percentage of marks scored by Q and V is 186. Sum Of the percentage of marks scored in HSC and SSC exams by Q is 160. One student scored 79% in SSC exam , the sum of the percentage of marks scored by T and R is not 168. Sum of the marks scored in HSC and SSC exams by R is not 152.

Eight persons- A to H are sitting around a rectangular table, where only one person is sitting on each of the shorter sides of the table and three persons are sitting on each of the longer sides of the table. All of them are facing towards the center of the table. Each of them obtained a different rank from 1 to 8 but they were not necessarily sitting in that order. It is also known that: The one who secured 1st rank is sitting opposite to F. G, who secured 2nd rank, is sitting to the immediate right of E, but they both do not sit on the same side of the table. The ones with ranks 1 and 8 are not adjacent to each other. C is sitting three places to the left of the one who secured 5th rank. The one who secured 5th rank is adjacent to the one who secured 6th rank. A is sitting opposite to the one who secured 8th rank. D is sitting four places to the left of G, but they are not opposite to each other. H is sitting to the immediate right of the one who secured 4^{th} rank. C and D are neither adjacent nor opposite to each other. Neither A nor B is sitting opposite to E. The sum of the ranks secured by B and H is not 10.

There are 8 students P1, P2, P3, P4, P5, P6, P7 and P8 staying in a building of 8 floors. The topmost floor in the building is the 8th floor while the bottommost floor is the 1st floor. All these students scored distinct marks (out of 100) 74, 75, 83, 89, 91, 92, 93 and 98 in Mathematics but not necessarily in the same order. The student staying on the topmost floor obtained even numbered marks. P2 obtained prime numbered marks and stays on the 7th floor. The difference between the marks obtained by the students staying on 1st and 2nd floor is 23. The difference between the marks obtained by the students staying on 6th and 7th floor is same as that of 7th and 8th floor. P4 stays on a floor that is just below the floor of the one who scored 74 marks. P7 obtained 93 marks and stays on an even numbered floor. P1 and P4 scored odd numbered marks and they live two floors away from each other. P5 stays on the second floor and obtained 75 marks. The difference between the marks obtained by the person living on the 6^{th} floor and 3^{rd} floor is less than that of 6^{th} floor and 5^{th} floor Only P2 and P3 stay on the floor above the floor of P6.